How do you solve the inequality |2x+3| > |x- 4|?

Feb 26, 2017

$x < - 7$ or $x > \frac{1}{3}$

Explanation:

$| 2 x + 3 | > | x - 4 |$ supposing $x \ne 4$ we have

$\left\mid \frac{2 x + 3}{x - 4} \right\mid > 1$ or equivalently

$- 1 < \frac{2 x + 3}{x - 4} < 1$ or

$- x + 4 < 2 x + 3 \to x > \frac{1}{3}$

or

$2 x + 3 < x - 4 \to x < - 7$

The feasible $x$ are:

$x < - 7$ or $x > \frac{1}{3}$